Ch. 2: The Quantum-

Mechanical Model of the Atom

Dr. Namphol Sinkaset

Chem 200: General Chemistry I

I. Chapter Outline

I. Introduction

II. The Wave Nature of Light

III. The Particle Nature of Light

IV. Bohr Model of the Atom

V. The Wave Nature of Matter

VI. The Quantum Mechanical Atom

I. Where are the Electrons?

• Where do more p+ go?

• What is the organization of the e- in the

atom?

• Since e- are responsible for chemical

reactivity, it’s an important question.

• Answer came from studying light.

II. Visible Light

• Visible light is a form of electromagnetic (EM)

radiation.

• All EM radiation consists of energy

propagated by electric and magnetic fields.

II. EM Radiation

• Different wavelengths indicate different types of EM radiation.

• Three characteristics of waves: amplitude, frequency, and wavelength

• Frequency and wavelength are related by the speed of light, 2.9979 x 108 m/s.

• c = nl

II. Visible Light

• White light is comprised of different colors.

• We observe the reflected light of objects.

II. The Electromagnetic Spectrum

II. Wave Properties of Light

• Waves of all types have certain

properties.

• interference: waves combine in different

ways to yield new waves

• diffraction: waves bend around

obstacles or slits that are similar in size

to their wavelength

• interference patterns: combo of both

II. Interference

II. Diffraction

II. Interference Patterns

III. Light as Particles?

• Everyone was happy with the wave explanation of light until puzzling observations were made.

• Explanations of these observations were put forth by people such as Planck, de Broglie, and Einstein.

• The photoelectric effect was the observation that really started the downfall classical EM theory.

III. The Photoelectric Effect

• No matter how bright the light, if it wasn’t the right n, it wouldn’t work!

• In 1905, Einstein proposed light had particles(!) of energy (photons). Ephoton = hn

IV. Electrons in Atoms

• The particle nature of light broke the

barrier between purely wave-like

behavior of EM radiation and small

particles in the atom.

• It was thought that particles in the atom

followed Newton’s laws of motion.

• New observations suggested matter

could behavior like waves!

IV. Atomic Line Spectra

IV. The Rydberg Equation

• People could not explain atomic spectra, but

in 1888, Rydberg presented an empirical

equation to predict the lines.

R = 1.097 x 107 m-1 and n2 > n1 (integers)

IV. Sample Problem 2.1

• If a ground state electron in a hydrogen

atom absorbs 2.10 x 10-18 J of energy,

to what energy level does it get excited?

Note that h = 6.626 x 10-34 J·s, c =

2.9979 x 108 m/s, and R = 1.097 x 107

m-1 .

IV. Bohr Model of the Atom

• Niels Bohr combined the ideas of Planck and Einstein for his model of H

1) H atom only has certain allowable energy levels – each level is a fixed circular orbit of e- around the nucleus, called a stationary state.

2) The atom doesn’t radiate energy if e-stays in its orbit (violates classical physics).

3) When e- changes orbit, it must emit or absorb energy to do so. The energy is exactly equal to the difference in energy of the orbits.

IV. Bohr Model of the Atom

V. Wave-Particle Duality

• Big conclusion: waves (EM radiation) can act

like a particle!

• In 1924, de Broglie proposed that matter (an

electron) must also be able to act like a wave!

• This idea was confirmed by experiments in

1927.

V. Particles as Waves, Really?

• If particles can act as waves, they should

show diffraction behavior…

V. The Wavy Electron

• Three important things arise from the

wave nature of electrons:

The de Broglie wavelength

The uncertainty principle

Indeterminacy

V. The de Broglie Wavelength

• The wavelength of a particle is related

to its kinetic energy.

• The faster it moves, the shorter its

wavelength.

V. Wavelengths of Particles

V. Behavior and Observation

• Wave-particle duality is a hard concept

to grasp.

• If an electron interferes with itself by

going through both slits, can’t we test

that?

• We can try…

V. Observation Changes the Result

• Electron detected through one slit or the

other, never both at once.

• Detection leads to disappearance of

interference pattern.

V. Finite Observation Powers

• We can’t observe both the particle

nature and the wave nature of the

electron at the same time.

• They are complementary properties; the

more we know about one, the less we

know about the other.

• Thus, when we observe, we see it as a

wave or a particle, not both.

V. Heisenberg Uncertainty

Principle

V. Probability Distribution Maps

• For normal size things, a moving particle has a definite location @ any instant.

• Electrons don’t behave this way, so you can’t know its exact location - indeterminacy.

• In chemistry, that means that in an atom, it’s impossible to know exactly where the e- are.

VI. A New Model of the Atom

• If velocity and position are

complementary properties, then energy

and position are as well.

• This means, we can know energy of an

electron in an atom, but not its position.

• Schrödinger develops his equation for

an electron in an atom in 1925.

VI. The Schrödinger Equation

• Y is the wave function of the e-, and it describes the state of the e- wave.

• The equation has multiple solutions, and each solution is a different wave function often referred to as an atomic orbital. The orbital is a map that shows where electron can be found.

• e- do not occupy atomic orbitals like orbits – AN ATOMIC ORBITAL IS AN ELECTRON!!

VI. Quantum Numbers

• A solution of the wavefunction (Y) yields 3 quantum numbers.

1) principal quantum number (n): a positive integer (1, 2, 3, etc.) that indicates the overall size and energy of the orbital

2) angular momentum quantum number (l): an integer from 0 to n-1 that’s related to the shape of the orbital

3) magnetic quantum number (ml): an integer from –l to +l that indicates orientation of the orbital relative to the nucleus

VI. Hierarchy of Quantum Numbers

VI. Quantum Number Terminology

• level: the n value gives the atom’s energy

levels or shells

• sublevel: each level contains sublevels or

subshells which have different shapes, each

with a letter designation

l = 0 is “s”

l = 1 is “p”

l = 2 is “d”

l = 3 is “f”

• orbital: each allowed combo of n, l, ml values

specifies one of the atom’s orbitals

VI. The 1s Orbital

VI. The 2s and 3s Orbitals

VI. The 2p Orbitals

VI. The 3d Orbitals

VI. The 4f Orbitals

VI. Orbital Phase

• Orbitals are 3-D waves, so they exhibit

phase just like 1-D waves.

• This becomes important in bonding.

VI. Energy Levels of H Atom

• For H atom, energy

states depend only

on n.

• For any other

element, energy

state depends on n

and l.